On a possible quantum contribution to the red shift

TL;DR

This paper explores how the quantum behavior of unstable states over long times could lead to a decrease in their energy, potentially affecting astrophysical observations and the interpretation of cosmic phenomena.

Contribution

It introduces a quantum mechanical model showing long-time energy corrections of unstable states, suggesting a possible quantum contribution to the cosmological red shift.

Findings

Energy of unstable states decreases at long times

Long-time energy corrections differ from short-time behavior

Potential impact on astrophysical and cosmological measurements

Abstract

We consider an effect generated by the nonexponential behavior of the survival amplitude of an unstable state in the long time region: In 1957 Khalfin proved that this amplitude tends to zero as $t$ goes to the infinity more slowly than any exponential function of $t$. This effect can be described in terms of time-dependent decay rate $\gamma(t)$ and then the Khalfin result means that this $\gamma(t)$ is not a constant for long times but that it tends to zero as $t$ goes to the infinity. It appears that a similar conclusion can be drawn for the energy of the unstable state for a large class of models of unstable particles: This energy should be much smaller for suitably long times $t$ than the energy of this state for $t$ of the order of the lifetime of the considered state. Within a given model we show that the energy corrections in the long ($t \to \infty$) and relatively short (lifetime of the state) time regions, are different. It is shown that these corrections decrease to ${\cal E} = {\cal E}_{min} < {\cal E}_{\phi}$ as $t \to \infty$, where ${\cal E}_{\phi}$ is the energy of the system in the state $|\phi>$ measured at times $t \sim \tau_{\phi}= \frac{\hbar}{\gamma}$. This is a purely quantum mechanical effect. It is hypothesized that there is a possibility to detect this effect by analyzing the spectra of distant astrophysical objects. The above property of unstable states may influence the measured values of astrophysical and cosmological parameters.